The longest increasing subsequence in a random permutation, the second class particle in TASEP, and semi-discrete polymers at zero temperature have the same scaling limit: a random function with Holder exponent 2/3-. This limit can be described in terms of the directed landscape, a random metric at the heart of the Kardar-Parisi-Zhang universality class.

In this talk I will give some insight into the construction of the directed landscape, which is joint work with Duncan Dauvergne and Janosch Ortmann.